Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x-3y &= -6 \\ -8x-6y &= -6\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = 8x-6$ Divide both sides by $-6$ to isolate $y$ $y = {-\dfrac{4}{3}x + 1}$ Substitute this expression for $y$ in the first equation. $-7x-3({-\dfrac{4}{3}x + 1}) = -6$ $-7x + 4x - 3 = -6$ Simplify by combining terms, then solve for $x$ $-3x - 3 = -6$ $-3x = -3$ $x = 1$ Substitute $1$ for $x$ back into the top equation. $-7( 1)-3y = -6$ $-7-3y = -6$ $-3y = 1$ $y = -\dfrac{1}{3}$ The solution is $\enspace x = 1, \enspace y = -\dfrac{1}{3}$.